We consider the question of taking transitive closures on top of pure relational systems (Sybase and Ingres in this case). We developed three kinds of transitive closure programs , one using a stored procedure to simulate a built-in transitive closure operator, one using the C language embedded with SQL statements to simulate the iterated execution of the transitive closure operation, and one u...

For a fixed k, an oriented graph is k-transitive if it is acyclic and for every directed path p=u1→u2→...→uk+2 with k+2 vertices, p induces a clique if each of the two subpaths u1→u2→...→uk+1 and u2→...→uk+2 induces a clique. We describe an algorithm to find a maximum weight clique in a k-transitive graph. Consider a hereditary family G of graphs. A graph H(V,E) is called G-k-mixed if its edge ...

An equivalent relation between transitive 1-factorizations of arctransitive graphs and factorizations of their automorphism groups is established. This relation provides a method for constructing and characterizing transitive 1-factorizations for certain classes of arc-transitive graphs. Then a characterization is given of 2-arc-transitive graphs which have transitive 1factorizations. In this c...

J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single non-permutation ...

We give several characterisations of strongly projective graphs which generalise in many respects odd cycles and complete graphs [7]. We prove that all known families of projective graphs contain only strongly projective graphs, including complete graphs, odd cycles, Kneser graphs and non-bipartite distance-transitive graphs of diameter d ≥ 3.

There are two central themes to research involving applications of probabilistic methods to partially ordered sets. The first of these can be described as the study of random partially ordered sets. Among the specific models which have been studied are: random labelled posets; random t-dimensional posets; and the transitive closure of random graphs. A second theme concentrates on the adaptation...

This paper finishes the classification of primitive affine distance-transitive graphs by dealing with the only case left open, namely where the generalized Fitting subgroup of the stabilizer of a vertex is a finite quasisimple group of classical Lie type defined over the characteristic dividing the number of vertices of the graph. All graphs that are found to occur are known.